We recall that an orientable Poisson manifold \(M\)  is said to be unimodular if the modular class
of the structure vanishes. The modular class is a first order cohomology class in the Poisson
cohomology complex of \(M\)  defined by a Poisson vector field, which measures the
existence of an invariant volume form for the flows of all Hamiltonian vector fields (see
[1]}). So, by Liouville's theorem, the modular class of a symplectic manifold is zero. Besides the importance of the
modular class in a Poisson manifold for dynamics, unimodularity has also been used to prove the
existence of a duality between Poisson homology and Poisson cohomology [2]}.
